This research investigates the stability of a two-wheeled vehicle model on the basis of numerical determination of full range of eigenvalues of a linear approximation matrix in the vicinity of the rectilinear driving mode. The received result was checked by numerical integration of the initial equations system of the disturbed motion of the model. The discrepancy of two research techniques is explained by the specialty of the considered mathematical model in which two pairs of complex conjugate eigenvalues close to each other are realized, that explains the emergence of standard derivations at calculating their numerical determination. The model is asymptotically stable in the range much wider than an operational interval (up to 100 m/s). In order to provide more intensive dampening of initial disturbances, it is possible to introduce additional resilient and damping elements between the trucks and the body in the design of the wheeled vehicle that will counteract the yaw mode of trucks.
LORRY CONVOY STABILITY TAKING INTO ACCOUNT THE SKEW OF SEMITRAILER AXESSummary. The mathematical model of a saddle-type lorry convoy is improved taking into account the skew of the axes of a semitrailer. It is shown that the motion of a lorry convoy without the skew of the axes is asymptotically steady. The skew of any axis of a semitrailer results in the worsening of stability of the rectilinear motion conditioned by the oscillations of the towed link. УСТОЙЧИВОСТЬ АВТОПОЕЗДА С УЧЕТОМ ПЕРЕКОСА ОСЕЙ ПОЛУПРИЦЕПААннотация. Усовершенствована математическая модель седельного автопоезда с учетом перекоса осей полуприцепа. Показано, что движение автопоезда без перекоса осей является асимптотически устойчивым. Перекос любой оси полуприцепа приводит к ухудшению устойчивости прямолинейного движения, обусловленного колебаниями прицепного звена.
The influence of design characteristics (elastic characteristics of tires and asymmetry of cornering forces) on the stability and handling of a vehicle is studied. The parameter continuation method is used to validate the results of constructing bifurcation sets in the space of two control parameters.Instable rectilinear motion of a vehicle model is the simplest partial case in the instability analysis of stable circular motions. In symmetric models of automobile and articulated truck [9], the critical velocity of circular motion tends to the critical velocity of rectilinear motion ν cr + as the drive wheel angle tends to zero. Moreover, as follows from singularity theory [1], the critical set in the neighborhood of ν cr + is described by a semicubical parabola.For local and global analyses of the bifurcation set (critical parameter set) of a symmetric vehicle model, the authors of [5,6] proposed methods that do not require preliminary determination of the equilibrium values of the phase variables. The present paper sets forth possible approaches to determine the critical set of an asymmetric vehicle model (in the presence of small perturbations disturbing the symmetry of the dynamic system with two control parameters, the critical set shifts, losing symmetry; finite perturbations may give rise to new dynamic properties of the model, which is manifested as a more complex bifurcation set).
The peculiarities of organization and perspectives of mass passenger transportation in the city and beyond are considered with the use of "Bus Rapid Transport" (BRT) or Metrobus. Different aspects of study of motor vehicles (MV) controllability and stability are analyzed. It is substantiated that it is sufficient to consider the potential stability of the MV itself, in order to guarantee the stability of the "driver MV" system with a large reserve. A mathematical model of a three-axle bus train consisting of a bus and two trains (metrobus) is developed and the factors influencing the critical speed as the main index of the stability of its movement are determined. It is established that the increase of the critical speed of the metrobus can be achieved by increasing the base of the bus, the first and the second trailer, as well as the mass of the bus and the coefficients of resistance of the drive wheels of the bus driving axle and the trailers axles. At the same time, increasing the distance from the mass center to the bus rear axle, increasing the distance from the mass center to the point of the coupling of the bus with the first trailer, increasing the mass of trailers and the resistance of the resistance of the wheel drive of the bus axis lead to a decrease in the critical speed of the metrobus. This must be taken into account both when designing metrobuses, and when operating them.
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